Rodgers has been at the helm of the club since February.
Brendan Rodgers says he is fully committed to the club and any speculation linking him with Manchester United is not real.
Rodgers is said to be United's number one choice to replace Solskjaer.
The speculation is disrespectful, the 48 year old has said.
Rodgers said he was proud to be the manager and fully committed to the job.
I can't comment on it because it isn't real. We can't control the other noise around that.
In recent years, the former manager of the Reds has been linked with a number of other teams, including the likes of Spurs,Spurs andNewcastle.
Rodgers said it was disrespectful to ask about replacing Solskjaer when there was a good manager and a good man working hard at the club.
The 12th place team in the league has 15 points from 11 games. Rodgers wants to stop the rumors from having a negative effect on his squad.
The Northern Irishman said that it doesn't bother him because he always looks for the next game. I'm only thinking about the club that I'm about to play.
It's frustrating for our supporters and my players. If anyone is to read anything out there, that can cause a lot of trouble.
It's part of the modern game, lots of speculation and gossip, but it's not something I have any focus on.
